High-efficiency multi-slot waveguide nano-opto-electromechanical phase modulator

ABSTRACT

A nano-opto-electro-mechanical System (NOEMS) phase shifter is described. The NOEMS may include a multi-slot waveguide structure suspended in air. The multi-slot waveguide structure may include three or more waveguides separated from each other by slots. The width of the slots may be sufficiently small to support slot modes, where a substantial portion of the mode energy is within the slots. For example, the slots may have widths less than 200 nm or less than 100 nm. The multi-slot waveguide structure may be disposed in a trench formed though the upper cladding of a substrate. An undercut may be formed under the multi-slot waveguide structure to enable free motion of the structure. NOEMS phase modulators of the types described herein may be used in connection with photonic processing systems, telecom/datacom systems, analog systems, etc.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application is a Continuation claiming the benefit under 35 U.S.C.§ 120 of U.S. patent application Ser. No. 16/411,476, entitled“HIGH-EFFICIENCY MULTI-SLOT WAVEGUIDE NANO-OPTO-ELECTROMECHANICAL PHASEMODULATOR,” filed on May 14, 2019 under Attorney Docket No.L0858.70006US01, which is hereby incorporated herein by reference in itsentirety.

U.S. patent application Ser. No. 16/411,476 claims the benefit under 35U.S.C. § 119(e) to U.S. Provisional Application Ser. No. 62/792,720,entitled “HIGH-EFFICIENCY DOUBLE-SLOT WAVEGUIDENANO-OPTOELECTROMECHANICAL PHASE MODULATOR,” filed on Jan. 15, 2019under Attorney Docket No. L0858.70006US00, which is hereby incorporatedherein by reference in its entirety.

BACKGROUND

Phase modulators are optical devices designed to vary the phase ofoptical signals. In phase modulators, phase changes can be achieved byvarying the refractive index of a material. Examples of mechanism forachieving refractive index variations include the free-carrier plasmadispersion and the thermo-optic effect. The free-carrier plasmadispersion effect is related to the density of free carriers in asemiconductor, which causes changes both in the real and imaginary partsof the refractive index. Hence, phase modulation can be achieved bycarrier injection or depletion. The thermo-optic effect is related tochanges in the refractive index of a material responsive to temperaturechanges. Typical thermo-optic phase modulators include dopedsemiconductor regions, in which a temperature rise results from thepassage of electric charges.

SUMMARY OF THE DISCLOSURE

Some embodiments relate to a photonic apparatus comprising a substrate;an input optical waveguide formed on the substrate; and a suspendedmulti-slot optical structure optically coupled to the input opticalwaveguide.

In some embodiments, the suspended multi-slot optical structurecomprises first, second and third optical waveguides arranged to form afirst slot between the first optical waveguide and the second opticalwaveguide and a second slot between the second optical waveguide and thethird optical waveguide.

In some embodiments, the first, second and third optical waveguides areco-planar.

In some embodiments, the first slot is sized to support more opticalenergy than the third optical waveguide.

In some embodiments, the first slot has a width that is equal to or lessthan 200 nm.

In some embodiments, the first slot has a width that is equal to or lessthan 100 nm.

In some embodiments, the second optical waveguide is contiguous with theinput waveguide.

In some embodiments, the second optical waveguide is tapered such thatthe width of the second waveguide is equal to a width of the inputwaveguide at a distal end of the suspended multi-slot optical structureand the width of the second waveguide is less than a width of the inputwaveguide at a center of the suspended multi-slot optical structure.

In some embodiments, the suspended multi-slot optical structure issurrounded by air.

In some embodiments, the suspended multi-slot optical structure is freeto oscillate in the air relative to the substrate.

In some embodiments, the suspended multi-slot optical structure is freeto oscillate in a direction perpendicular to a propagation axis of thesuspended multi-slot optical structure.

In some embodiments, the photonic apparatus further comprises a lowercladding formed on the substrate and an undercut formed through aportion of the lower cladding between the substrate and the suspendedmulti-slot optical structure.

In some embodiments, the lower cladding is not in contact with thesuspended multi-slot optical structure.

In some embodiments, the photonic apparatus further comprises an uppercladding formed on the lower cladding and a trench formed through aportion of the upper cladding, wherein the suspended multi-slot opticalstructure is disposed in the trench.

In some embodiments, at least a portion of the input optical waveguiderests on the lower cladding.

In some embodiments, the suspended multi-slot optical structure is madeof a material having a doping concentration less than 10¹⁴ cm⁻³.

In some embodiments, the suspended multi-slot optical structure is madeof an undoped material.

Some embodiments relate to an optical phase shifter comprising asubstrate; an input optical waveguide formed on the substrate; an outputoptical waveguide formed on the substrate; and a multi-slot opticalstructure optically coupling the input optical waveguide to the outputoptical waveguide and forming first and second slots.

In some embodiments, the multi-slot optical structure comprises first,second and third optical waveguides, the first slot being formed betweenthe first and second optical waveguides and the second slot being formedbetween the second and third optical waveguides.

In some embodiments, the mechanical structure is attached to the firstand third optical waveguides.

In some embodiments, motion of the mechanical structure causes avariation in a width of the first slot and/or a variation in a width ofthe second slot.

In some embodiments, the multi-slot optical structure has a length thatis less than or equal to 50 μm.

In some embodiments, the multi-slot optical structure has a length thatis less than or equal to 30 μm.

In some embodiments, the multi-slot optical structure is suspended.

In some embodiments, the optical phase shifter further comprises a lowercladding formed on the substrate and an undercut formed through aportion of the lower cladding between the substrate and the multi-slotoptical structure.

In some embodiments, the lower cladding is not in contact with themulti-slot optical structure.

In some embodiments, the optical phase shifter further comprises anupper cladding formed on the lower cladding and a trench formed though aportion of the upper cladding, wherein the multi-slot optical structureis disposed in the trench.

In some embodiments, the optical phase shifter further comprises amechanical structure connecting the multi-slot optical structure to amechanical driver.

Some embodiments relate to a method for shifting a phase of an opticalsignal, the method comprising providing the optical signal to amulti-slot optical structure formed on a substrate and having first andsecond slots; exciting a multi-slot optical mode defined in themulti-slot optical structure; and varying a width of the first slotand/or a width of the second slot over time.

In some embodiments, at least 50% of an energy of the multi-slot mode iswithin the first and second slots.

In some embodiments, varying a width of the first slot and/or a width ofthe second slot over time comprises applying a mechanical force to themulti-slot optical structure via a mechanical structure.

In some embodiments, the multi-slot optical structure comprises first,second and third optical waveguides, wherein the first slot is formedbetween the first and second optical waveguides and the second slot isformed between the second and third optical waveguides, and whereinapplying a mechanical force to the multi-slot optical structurecomprises applying a mechanical force to the first optical waveguide andthe third optical waveguide.

Some embodiments relate to a method for fabricating a photonicapparatus, the method comprising obtaining a chip having a substrate, alower cladding layer formed on the substrate, a semiconductor layerformed on the lower cladding layer and an upper cladding layer formed onthe semiconductor layer; patterning the semiconductor layer to form amulti-slot optical structure having first and second slots; forming atrench in the upper cladding layer to expose the multi-slot opticalstructure to air; and forming an undercut in the lower cladding layer tosuspend at least a portion of the multi-slot optical structure in air.

In some embodiments, patterning the semiconductor layer to form themulti-slot optical structure comprises patterning the semiconductorlayer to form first, second and third optical waveguides, the first slotbeing disposed between the first and second optical waveguides and thesecond slot being disposed between the second and third opticalwaveguides.

In some embodiments, forming the trench in the upper cladding layercomprises performing a reactive ion etch through the upper claddinglayer.

In some embodiments, forming the undercut in the lower cladding layercomprises performing an isotropic etch through the lower cladding layer.

Some embodiments relate to a nano-opto-electro-mechanical System (NOEMS)phase shifter comprising: a plurality of non-conductive waveguidessuspended in a trench.

In some embodiments, each of the plurality of non-conductive waveguideshas a resistivity greater than 1300 Ωcm.

In some embodiments, adjacent waveguides of the plurality ofnon-conductive waveguides are separated from each other by less than 200nm.

In some embodiments, the NOEMS phase shifter further comprises amechanical driver configured to cause oscillation of at least some ofthe plurality of non-conductive waveguides.

BRIEF DESCRIPTION OF THE DRAWINGS

Various aspects and embodiments of the application will be describedwith reference to the following figures. It should be appreciated thatthe figures are not necessarily drawn to scale. Items appearing inmultiple figures are indicated by the same reference number in all thefigures in which they appear.

FIG. 1A is a top view illustrating schematically aNano-Opto-Electromechanical Systems (NOEMS) phase modulator, inaccordance with some non-limiting embodiments.

FIG. 1B is a top view illustrating schematically a suspended multi-slotoptical structure of the NOEMS phase modulator of FIG. 1A, in accordancewith some non-limiting embodiments.

FIG. 1C is a plot illustrating an example of an optical mode arising inthe suspended multi-slot optical structure of FIG. 1B, in accordancewith some non-limiting embodiments.

FIG. 1D is a top view illustrating schematically a mechanical structureof the NOEMS phase modulator of FIG. 1A, in accordance with somenon-limiting embodiments.

FIG. 1E is a top view illustrating schematically a transition region ofthe NOEMS phase modulator of FIG. 1A, in accordance with somenon-limiting embodiments.

FIG. 2 is a cross-sectional view of the NOEMS phase modulator of FIG.1A, taken in a yz-plane, and illustrating a suspended waveguide, inaccordance with some non-limiting embodiments.

FIG. 3 is a cross-sectional view of the NOEMS phase modulator of FIG.1A, taken in a xy-plane, and illustrating a portion of a suspendedmulti-slot optical structure, in accordance with some non-limitingembodiments.

FIGS. 4A-4C are cross-sectional views illustrating how a suspendedmulti-slot optical structure can be mechanically driven to vary thewidths of the slots between the waveguides, in accordance with somenon-limiting embodiments.

FIG. 5 is a plot illustrating how the effective index of a suspendedmulti-slot optical structure may vary as a function of the width of aslot, in accordance with some non-limiting embodiments.

FIG. 6 is a flowchart illustrating an example of a method forfabricating a NOEMS phase modulator, in accordance with somenon-limiting embodiments.

DETAILED DESCRIPTION

The inventors have recognized and appreciated that certain optical phasemodulators suffer from high dynamic loss and low modulation speed, whichsignificantly limit the range of applications in which these phasemodulators can be deployed. More specifically, some phase modulatorsinvolve significant trade-offs between modulation speed and dynamicloss, such that an increase in modulation speed results in an increasein dynamic loss. As used herein, the phrase “dynamic loss” refers tooptical power loss experienced by an optical signal that depends on thedegree to which its phase is modulated. Ideal phase modulators are suchthat power loss is independent of the phase modulation. Real-world phasemodulators, however, experience a certain power loss when no modulationoccurs, and experience a different power loss when modulation occurs.For example, the power loss experienced at no phase modulation may beL₁, the power loss experienced at a π/2-phase modulation may be L₂, andthe power loss experienced at a π-phase modulation may be L₃, with L₁,L₂ and L₃ being different from each other. This behavior is undesirablebecause, in addition to phase modulation, the signal further experiencesamplitude modulation.

Some such phase modulators, in addition, require several hundreds ofmicrons in length to provide sufficiently large phase shifts.Unfortunately, being so long, such phase modulators are not suitable foruse in applications requiring integration of several phase shifters on asingle chip. The phase modulators alone may take up most of the spaceavailable on the chip, thus limiting the number of devices that can beco-integrated on the same chip.

Recognizing the aforementioned limitations of certain phase modulators,the inventors have developed small footprint-optical phase modulatorscapable of providing high modulation speeds (e.g., in excess of 100 MHzor 1 GHz) while limiting dynamic loss. In some embodiments, a phasemodulator may occupy an area as small as 300 m². Thus, as an example, areticle having an area of 1 cm² can accommodate as many as 15,000 phasemodulators while saving an additional 50 mm² for other devices.

Some embodiments relate to Nano-Opto-Electromechanical Systems (NOEMS)phase modulators having multiple suspended optical waveguides positionedadjacent to one another and forming a plurality of slots therebetween.The dimensions of the slots are sufficiently small to form slotwaveguides, whereby a substantial portion (e.g., a majority) of the modeenergy is confined in the slots themselves. These modes are referred toherein as slot modes. Having a substantial portion of the mode energy inthe slots enables modulation of the effective index of the mode, and aresult, of the phase of an optical signal embodying the mode, by causingvariations in the dimensions of the slots. In some embodiments, phasemodulation can be achieved by applying mechanical forces that causevariations in the dimensions of the slots.

The inventors have recognized and appreciated that the modulation speedachievable with the NOEMS phase modulators described herein can beincreased, without significant increases in dynamic loss, by decouplingthe mechanical drivers from the region where optical modulation takesplace. In phase modulators in which the mechanical drivers are decoupledfrom the optical modulation region, electric driving signals are appliedon the mechanical drivers, rather than being applied on the opticalmodulation region itself. This arrangement removes the need to make theoptical modulation region electrically conductive, thus enabling areduction in the doping of this region. The low doping results in areduction of free carriers which may otherwise lead to opticalabsorption, thus lowering dynamic loss.

Furthermore, decoupling the mechanical drivers from the opticalmodulation region enables a greater modulation per unit length, and as aresult a shorter modulation region. Shorter modulation regions, in turn,enable, greater modulation speed.

The inventors have further recognized and appreciated that includingmultiple slots in the modulation region can enable a further reductionin the length of the phase modulator (thereby decreasing its size).Having more than one slot, in fact, enables a substantial reduction inthe length of the transition region through which light is coupled tothe modulation region. The result is a substantially more compact formfactor. Thus, NOEMS phase modulators of the types described herein canhave shorter modulation regions and/or shorter transition regions. Phasemodulators of the types described herein can have lengths as low as 20μm or 30 μm, in some embodiments.

As will be described in detail further below, some embodiments relate tophase modulators in which a trench is formed in the chip, and isarranged so that the modulating waveguides are suspended in air and arefree move in space.

The inventors have recognized a potential drawback associated with theuse of trenches that results from the formation of cladding/airinterfaces. When a propagating optical signal enters (or exits) atrench, it encounters a cladding/air interface (or an air/claddinginterface). Unfortunately, the presence of the interface can give riseto optical reflections, which in turn can increase insertion losses. Theinventors have appreciated that the negative effect of such interfacescan be mitigated by reducing the physical extension of the optical modein the region where it passes through the interface. This can beachieved in various ways. For example, in some embodiments, theextension of the optical mode may be reduced by tightly confining themode within a rib waveguide. A rib waveguide may be sized so that only asmall fraction of the mode energy (e.g., less than 20%, less than 10%,or less than 5%) is outside the edges of the waveguide.

NOEMS phase modulators of the types described herein may be used in avariety of applications, including for example in telecom and datacom(including local area networks, metropolitan area networks, wide areanetworks, data center networks, satellite networks, etc.), analogapplications such as radio-over-fiber, all-optical switching, coherentLidar, phased arrays, coherent imaging, machine learning and other typesof artificial intelligence applications. Additionally, the NOEMSmodulators may be used as part of amplitude modulators, for example ifcombined with a Mach Zehnder modulator. For example, a Mach Zehndermodulator may be provided in which a NOEMS phase modulator is positionedin one or more of the arms of the Mach Zehnder modulator. Severalmodulation schemes may be enabled using NOEMS phase modulators,including for example amplitude shift keying (ASK), quadrature amplitudemodulation (QAM), phase shift keying (BPSK), quadrature phase shiftkeying (QPSK) and higher order QPSK, offset quadrature phase-shiftkeying (OQPSK), Dual-polarization quadrature phase shift keying(DPQPSK), amplitude phase shift keying (APSK), etc. Additionally, NOEMSphase modulators may be used as phase correctors in applications inwhich the phase of an optical signal tends to drift unpredictably. Insome embodiments, NOEMS phase modulators of the types described hereinmay be used as part of a photonic processing system.

FIG. 1A is a top view illustrating schematically aNano-Opto-Electromechanical Systems (NOEMS) phase modulator, inaccordance with some non-limiting embodiments. NOEMS phase modulator 100includes input waveguide 102, output waveguide 104, input transitionregion 140, output transition region 150, suspended multi-slot opticalstructure 120, mechanical structures 130 and 132, and mechanical drivers160 and 162. NOEMS phase modulator 100 may be fabricated using siliconphotonic techniques. For example, NOEMS phase modulator 100 may befabricated on a silicon substrate, such as a bulk silicon substrate or asilicon-on-insulator (SOI) substrate. In some embodiments, NOEMS phasemodulator 100 may further include electronic circuitry configured tocontrol the operations of mechanical drivers 160 and 162. The electroniccircuitry may be fabricated on the same substrate hosting the componentsof FIG. 1A, or on a separate substrate. When disposed on a separatesubstrate, the substrates may be bonded to one another in a any suitableway, including 3D-bonding, flip-chip bonding, wire bonding etc.

At least part of NOEMS phase modulator 100 is formed in a trench 106. Aswill be described in detail further below, trenches of the typesdescribed herein may be formed by etching a portion of the cladding. Inthe example of FIG. 1A, trench 106 has a rectangular shape, thoughtrenches of any other suitable shape may be used. In this example,trench 106 has four sidewalls. Sidewalls 112 and 114 are spaced from oneanother along the z-axis (referred to herein as the propagation axis),and the other two sidewalls (not labeled in FIG. 1A) are spaced from oneanother along the x-axis.

In some embodiments, the separation along the z-axis between sidewalls112 and 114 may be less than or equal to 50 μm, less than or equal to 30μm, or less than or equal to 20 μm. Thus, the modulation region of thisNOEMS phase modulator is significantly shorter than other types of phasemodulators, which require several hundreds of microns for modulating thephase of an optical signal. The relatively short length is enable by oneor more of the following factors. First, having multiple slots improvescoupling to the optical modulation region, which in turn enables areduction in the length of the transition region. The improved couplingmay be the result of enhanced mode symmetry in the multi-slot structure.Second, decoupling the mechanical drivers from the optical modulationregion enables a greater modulation per unit length, and as a result ashorter modulation region.

During operation, an optical signal may be provided to input waveguide102. In one example, the optical signal may be a continuous wave (CW)signal. Phase modulation may take place in suspended multi-slot opticalstructure 120. A phase modulated optical signal may exit NOEMS phasemodulator 100 from output waveguide 104. Transition region 140 mayensure loss-free or nearly loss-free optical coupling between inputwaveguide 102 and suspended multi-slot optical structure 120. Similarly,transition region 150 may ensure loss-free or nearly loss-free opticalcoupling between suspended multi-slot optical structure 120 and outputwaveguide 104. Transitions regions 140 and 150 may include taperedwaveguides in some embodiments, as described in detail further below. Asdiscussed above, the length of the transitions regions may be shorterrelative to other implementations.

The input optical signal may have any suitable wavelength, including butnot limited to a wavelength in the O-band, E-band, S-band, C-band orL-band. Alternatively, the wavelength may be in the 850 nm-band or inthe visible band. It should be appreciated that NOEMS phase modulator100 may be made of any suitable material, so long as the material istransparent or at least partially transparent at the wavelength ofinterest, and the refractive index of the core region is greater thanthe refractive index of the surrounding cladding. In some embodiments,NOEMS phase modulator 100 may be made of silicon. For example, inputwaveguide 102, output waveguide 104, input transition region 140, outputtransition region 150, suspended multi-slot optical structure 120, andmechanical structures 130 and 132 may be made of silicon. Givensilicon's relatively low optical bandgap (approximately 1.12 eV),silicon may be particularly suitable for use in connection with nearinfrared wavelengths. In another example, NOEMS phase modulator 100 maybe made of silicon nitride or diamond. Given silicon nitride's anddiamond's relatively high optical bandgaps (approximately 5 eV andapproximately 5.47 eV, respectively), these materials may beparticularly suitable for use in connection with visible wavelengths.However, other materials are also possible, including indium phosphide,gallium arsenide, and or any suitable III-V or II-VI alloy.

In some embodiments, input waveguide 102 and output waveguide 104 may besized to support a single mode at the wavelength of operation (thoughmulti-mode waveguides can also be used). For example, if a NOEMS phasemodulator is designed to operate at 1550 nm (though of course, not allembodiments are limited in this respect), input and output waveguides102 and 104 may support a single mode at 1550 nm. In this way, the modeconfinement within the waveguide may be enhanced, thus reducing opticallosses due to scattering and reflections. Waveguides 102 and 104 may berib waveguides (e.g., with rectangular cross sections) or may have anyother suitable shape.

As described above, part of NOEMS phase modulator 100 may be formedwithin a trench 106, so that the waveguides in the modulation region aresurrounded by air and are free to move in space. The drawback ofincluding a trench is the formation of a cladding/air interface and anair/cladding interface along the propagation path. Thus, the inputoptical signal passes a cladding/air interface (in correspondence withsidewall 112) before reaching the region where modulation occurs andpasses an air/cladding interface (in correspondence with sidewall 114)after the modulation region. These interfaces may introduce reflectionlosses. In some embodiments, reflection losses may be reduced bypositioning transition region 140 inside, rather than outside, trench106 (as shown in FIG. 1A). In this way, the mode expansion associatedwith the transition region takes place where the optical signal hasalready passed the cladding/air interface. In other words, the mode istightly confined as it passes the cladding/air interface, but isexpanded in the trench, using the transition region, for purposes ofcoupling to the suspended multi-slot structure 120. Similarly,transition region 150 may be formed inside trench 106, thereby spatiallyre-confining the mode before it reaches sidewall 114.

FIG. 1B illustrates suspended multi-slot optical structure 120 inadditional detail, in accordance with some non-limiting embodiments. Inthe example of FIG. 1B, multi-slot optical structure 120 includes threewaveguides (121, 122 and 123). Slot 124 separates waveguide 121 fromwaveguide 122 and slot 125 separates waveguide 122 from waveguide 123.The width of the slots (d₁ and d₂) may be less than the critical width(at the wavelength of operation) for forming slot modes, whereby asubstantial portion of the mode energy (e.g., more than 40%, more than50%, more than 60%, or more than 75%) is within the slots. For example,each of d₁ and d₂ may be equal to or less than 200 nm, equal to or lessthan 150 nm, or equal to or less than 100 nm. The minimum width may beset by the photolithographic resolution.

FIG. 1C is a plot illustrating an example of an optical mode supportedby the waveguides 121, 122 and 123, in accordance with some non-limitingembodiments. More specifically, the plot illustrates the amplitude of amode (e.g., the electric field E_(x), E_(y) or E_(z), or magnetic fieldH_(x), H_(y) or H_(z),). As illustrated, a substantial portion of theoverall energy is confined within the slots, where the mode exhibitspeaks of amplitude. In some embodiments, there is more optical energy inone of the slots than in any one of the individual waveguides. In someembodiments, there is more optical energy in one of the slots than inall the waveguides considered together. Outside the outer walls of theexterior waveguides, the mode energy decays (for example exponentially).

Widths d₁ and d₂ may be equal to, or different than, one another. Thewidths of the slots and the waveguides may be constant along the z-axis(as in FIG. 1B) or may vary. In some embodiments, the widths ofwaveguides 121, 122 and 123 may be less than the width of inputwaveguide 102. In some embodiments, when the wavelength of operation isin the C-band, the widths of waveguides 121, 122 and 123 may be between200 nm and 400 nm, between 250 nm and 350 nm, or within any othersuitable range, whether within or outside such ranges.

While the example of FIG. 1B illustrates suspended a multi-slot opticalstructure 120 with three waveguides and two slots, any other suitablenumber of waveguides and slots may be used. In other examples, asuspended multi-slot optical structure 120 may include five waveguidesand four slots, seven waveguides and six slots, nine waveguides andeight slots, etc. In some embodiments, the structure includes an oddnumber of waveguides (and consequently, an even number of slots) so thatonly symmetric modes are excited, while antisymmetric modes remainunexcited. The inventors have appreciated that enhancing the symmetry ofthe mode enhances coupling into the slotted structure, thus enabling asubstantial reduction in the length of the transition region. However,implementations with even number of waveguides are also possible.

As will be described in detail further below, phase modulation occurs bycausing the exterior waveguides (121 and 123 in FIG. 1B) to moverelative to the center waveguide (122 in FIG. 1B) along the x-axis. Whenwaveguide 121 moves in the x-axis relative to waveguide 122, the widthof slot 124 varies, and the shape of the mode supported by the structurevaries accordingly. The result is a change in the effective index of themode supported by the structure, and consequently, a phase modulationtakes place. Motion of the exterior waveguides may be induced usingmechanical structures 130 and 132.

An example of a mechanical structure 130 is illustrated in FIG. 1D, inaccordance with some non-limiting embodiments. Mechanical structure 132(see FIG. 1A) may have a similar arrangement. In the example of FIG. 1D,mechanical structure 130 includes beams 133, 134, 135 and 136. Beam 133connects mechanical driver 160 to beam 134. Beams 135 and 136 connectbeam 134 to the exterior waveguide. To limit optical losses, beams 135and 136 may be attached to the exterior waveguide in the transitionregions 140 and 150, respectively, rather than in the modulation region(as shown in FIG. 1E, which is discussed below). However, attachingbeams 135 and 136 to the exterior waveguide to the modulation region isalso possible. Beams with different shapes, sizes and orientations maybe used in alternative or in addition to those illustrated in FIG. 1D.

Mechanical structure 130 may transfer mechanical forces generated atmechanical driver 160 to waveguide 121, thereby causing waveguide 121 tomove relative to waveguide 122. Mechanical drivers 160 and 162 may beimplemented in any suitable way. In one example, the mechanical driversmay include piezoelectric devices. In one example, the mechanicaldrivers may include conductive fingers. When a voltage is appliedbetween adjacent fingers, the fingers may experience acceleration, thusimparting a mechanical force to the mechanical structures. In someembodiments, the mechanical drivers may be driven with an electricalsignal having a pattern encoded thereon. In this way, modulation resultsin the pattern being imparted onto the phase of an input optical signal.

It should be appreciated that, because the waveguides of suspendedmulti-slot optical structure 120 are driven using external mechanicaldrivers, rather than being directly supplied with electrical signals asin certain conventional phase modulators, the conductivity of thewaveguides can be relaxed, thus reducing free carrier absorption loss,and consequently, dynamic loss. This is different than some conventionalphase modulators, where the waveguide itself is doped to act as a heateror a carrier accumulation region. In some embodiments, waveguides 121,122 and 123 may be made of an undoped, or low-doped, semiconductormaterial (e.g., undoped silicon or silicon with a doping concentrationless than 10¹⁴ cm⁻³). In some embodiments, the resistivity of thematerial forming the waveguides may be greater than 1300 Ωcm.

FIG. 1E illustrates an example of a transition region 140, in accordancewith some non-limiting embodiments. In this implementation, waveguide122 is contiguous to (e.g., is the continuation of) input waveguide 102.As shown, waveguide 122 is tapered in the transition region such thatits width reduces as it approaches the suspended multi-slot opticalstructure 120. By contrast, waveguides 121 and 123 are tapered in thetransition region such that their widths increase as they depart fromsuspended multi-slot optical structure 120. The tapered waveguides mayallow adiabatic coupling between the mode of input waveguide 102 and themode of suspended multi-slot optical structure 120, thereby limitingcoupling losses. A similar arrangement may be used for transition region150. Due to the enhanced symmetry of the mode supported by themulti-slot structure, transition regions 140 and 150 are significantlyshorter than other implementations. In some embodiments, the transitionregions may be as short as 10 μm or less, or 5 μm or less, though othervalues are also possible.

FIG. 2 is a cross sectional view of a NOEMS phase modulator 100 taken ina yz-plane passing through waveguide 122 (see plane 190 in FIG. 1B), inaccordance with some non-limiting embodiments. Input waveguide 102 andoutput waveguide 104 are surrounded by a cladding made of a material(e.g., silicon oxide) with a refractive index lower than the refractiveindex of the core material. Lower cladding 202 is between the waveguideand the underlying substrate 201. Upper cladding 206 is formed over thewaveguide.

To enable free motion of the waveguides of the suspended multi-slotoptical structure 120, a trench 106 is formed through part of uppercladding 206. In some embodiments, a portion of the lower cladding 202is removed under the suspended multi-slot optical structure 120, thusforming an undercut 204. As a result, waveguides 121, 122 and 123 aresuspended in air and are free to move responsive to mechanical forces. Acladding/air interface exists at trench sidewall 112 and an air/claddinginterface exists at trench sidewall 114. The sidewalls may besubstantially vertical, for example if the trench is formed by reactionion etching (RIE), or may alternatively be angled. Undercut 204 may havecurved sidewalls, as illustrated in FIG. 2, if an isotropic etch isused, or may alternatively be substantially vertical. In someembodiments, trench 106 and undercut 204 may be formed as part of thesame etch, while in other embodiments, they be formed using separateetches.

FIG. 3 is a cross sectional view of a NOEMS phase modulator 100 taken ina xy-plane passing through waveguides 121, 122 and 123 (see plane 191 inFIG. 1B), in accordance with some non-limiting embodiments. FIG. 3 showsthat waveguides 121, 122 and 123 and beams 134, are co-planar (at leastin this example), and are suspended in air above substrate 201. Asfurther illustrated in this figure, waveguides 121, 122 and 123 do notcontact lower cladding 202 at this cross section. When mechanicaldrivers 160 and 162 are actuated, beams 134 and waveguides 121 and 123oscillate along the x-axis, thus varying the widths of the slots 124 and125. An example of an oscillatory motion of waveguides 121 and 123 isillustrated, collectively, in FIGS. 4A-4C, in accordance with somenon-limiting embodiments. FIG. 4A illustrates a case in which nomechanical force is applied. As a result, the widths of the slots areunperturbed. In FIG. 4B, a pair of forces is applied such that bothwaveguides 121 and 123 move towards waveguide 122, as illustrated by thearrows. As a result, the widths of the slots are reduced. In FIG. 4C, apair of forces is applied such that both waveguides 121 and 123 moveaway from waveguide 122, also illustrated by the arrows. As a result,the widths of the slots are increased. In some embodiments, the forcesmay be applied in a periodic fashion, and/or following the pattern ofthe driving electrical signals. In some embodiments, the forces may beapplied to waveguides 121 and 123 differentially, such that the sameintensity is applied to both waveguides but with opposite signs.

FIG. 5 is a plot illustrating how the effective refractive index (Neff)of the mode propagating in the suspended multi-slot optical structure120 varies as a function of width d₁ (the width of the slot betweenwaveguides 121 and 122), in accordance with some non-limitingembodiments. A similar response may be plotted as a function of d₂. Theeffective index variation is caused by the fact that, as the separationbetween the waveguides varies under the effect of an applied mechanicalforce, the shape of the mode deviates relative to the one illustrated inFIG. 1C. As the width varies over time, so does the mode effectiveindex, and consequently, the phase of the mode.

FIG. 6 is a flowchart illustrating an example of a method forfabricating a NOEMS phase modulator, in accordance with somenon-limiting embodiments. It should be appreciated that the steps of themethod described below may be performed in any suitable order, asfabrication processes are not limited to the specific order illustratedin FIG. 6.

Fabrication method 600 begins at step 602, in which a chip is obtained.In some embodiments, the chip may be a silicon-on-insulator chip, or abulk silicon chip. The chip may have a substrate and any of thefollowing layers: a lower cladding layer, a semiconductor layer and anupper cladding layer. The lower cladding layer may comprise siliconoxide in some embodiments. The semiconductor layer may comprisessilicon, silicon nitride and/or doped silicon oxide in some embodiments.The upper cladding layer may comprise the same material forming thelower cladding layer, or a different material. FIG. 3. Illustrates anexamples of a substrate (substrate 201) having a lower cladding layer(cladding 202), a semiconductor layer (the layer of waveguides 121, 122and 123) and an upper cladding layer (cladding 206). It should beappreciated that any of the layers identified above may already bepresent on the chip when the chip arrives at the fabrication facility(where the NOEMS phase modulator is fabricated), or may be formed at thefacility as part of the fabrication process.

At step 604, the semiconductor layer is patterned form a multi-slotoptical structure having first and second slots (or any other number ofslots greater than two). In the example of FIG. 3, waveguides 121, 122and 123 may be formed at step 604. Patterning the semiconductor layermay involve deposition of a photoresist layer, a photolithographicexposure and etching through the semiconductor layer. In someembodiments, any one of mechanical structures 130 and 132, mechanicaldrivers 160 and 162, waveguides 102 and 104 and transition regions 140and 142 (see FIG. 1A) are fabricated as part of the samephotolithographic exposure, though not all embodiments are limited inthis respect as one or more separate photolithographic exposures may beused. In some embodiments, at step 604, mechanical drivers 160 may bedoped, for example using ion implantation. In some embodiments, themulti-slot optical structure may remain undoped.

At step 606, a trench may be formed through the upper cladding layer. Anexample of a trench (trench 106) is illustrated at FIG. 3. The trenchmay be formed, for example, using a dry etch such as a reactive ionetch. However, wet etches may alternatively or additionally be used.Formation of the trench may involve removal of a portion of the uppercladding layer in a region above the multi-slot optical structure formedat step 604. As a result, the multi-slot optical structure may beexposed, partially or entirely, to air.

At step 608, an undercut may be formed in the lower cladding layer. Anexample of an undercut (undercut 204) is illustrated at FIG. 3. Theundercut may be formed, for example, using a wet etch, though dry etchesmay alternatively or additionally be used. Formation of the undercut mayinvolve removal of a portion of the lower cladding layer in a regionunder the multi-slot optical structure. As a result, at least part ofthe multi-slot optical structure may be suspended over air.

Having thus described several aspects and embodiments of the technologyof this application, it is to be appreciated that various alterations,modifications, and improvements will readily occur to those of ordinaryskill in the art. Such alterations, modifications, and improvements areintended to be within the spirit and scope of the technology describedin the application. It is, therefore, to be understood that theforegoing embodiments are presented by way of example only and that,within the scope of the appended claims and equivalents thereto,inventive embodiments may be practiced otherwise than as specificallydescribed. In addition, any combination of two or more features,systems, articles, materials, and/or methods described herein, if suchfeatures, systems, articles, materials, and/or methods are not mutuallyinconsistent, is included within the scope of the present disclosure.

Also, as described, some aspects may be embodied as one or more methods.The acts performed as part of the method may be ordered in any suitableway. Accordingly, embodiments may be constructed in which acts areperformed in an order different than illustrated, which may includeperforming some acts simultaneously, even though shown as sequentialacts in illustrative embodiments.

All definitions, as defined and used herein, should be understood tocontrol over dictionary definitions, definitions in documentsincorporated by reference, and/or ordinary meanings of the definedterms.

The indefinite articles “a” and “an,” as used herein in thespecification and in the claims, unless clearly indicated to thecontrary, should be understood to mean “at least one.”

The phrase “and/or,” as used herein in the specification and in theclaims, should be understood to mean “either or both” of the elements soconjoined, i.e., elements that are conjunctively present in some casesand disjunctively present in other cases.

As used herein in the specification and in the claims, the phrase “atleast one,” in reference to a list of one or more elements, should beunderstood to mean at least one element selected from any one or more ofthe elements in the list of elements, but not necessarily including atleast one of each and every element specifically listed within the listof elements and not excluding any combinations of elements in the listof elements. This definition also allows that elements may optionally bepresent other than the elements specifically identified within the listof elements to which the phrase “at least one” refers, whether relatedor unrelated to those elements specifically identified.

The terms “approximately” and “about” may be used to mean within ±20% ofa target value in some embodiments, within ±10% of a target value insome embodiments, within ±5% of a target value in some embodiments, andyet within ±2% of a target value in some embodiments. The terms“approximately” and “about” may include the target value.

What is claimed is:
 1. A method for shifting a phase of an opticalsignal, the method comprising: providing the optical signal to amulti-slot optical structure formed on a substrate and having first,second and third optical waveguides arranged to form a first slotbetween the first optical waveguide and the second optical waveguide anda second slot between the second optical waveguide and the third opticalwaveguide; exciting a multi-slot optical mode defined in the multi-slotoptical structure, the multi-slot optical mode has a first peakamplitude in the first optical waveguide and a second peak amplitude inthe first slot, wherein the second peak amplitude is larger than thefirst peak amplitude; and varying a width of the first slot and/or awidth of the second slot over time.
 2. The method of claim 1, whereinthe first and second peak amplitudes are electric field peak amplitudes.3. The method of claim 1, wherein varying a width of the first slotand/or a width of the second slot over time comprises applying amechanical force to the multi-slot optical structure via a mechanicalstructure.
 4. The method of claim 3 wherein applying a mechanical forceto the multi-slot optical structure comprises: applying the mechanicalforce to the first optical waveguide and the third optical waveguide. 5.The method of claim 1, wherein varying a width of the first slot and/ora width of the second slot over time comprises: increasing the width ofthe first slot and, simultaneously, increasing the width of the secondslot.
 6. The method of claim 5, varying a width of the first slot and/ora width of the second slot over time further comprises: reducing thewidth of the first slot and, simultaneously, reducing the width of thesecond slot.
 7. The method of claim 1, wherein providing the opticalsignal to a multi-slot optical structure comprises adiabaticallycoupling the optical signal to the multi-slot optical structure using atapered optical waveguide.
 8. The method of claim 1, wherein themulti-slot optical mode is a symmetric mode.
 9. A method for modulatinga phase of an optical signal, the method comprising: providing theoptical signal to a multi-slot optical structure formed on a substrateand having first, second and third co-planar suspended opticalwaveguides arranged to form a first slot between the first opticalwaveguide and the second optical waveguide and a second slot between thesecond optical waveguide and the third optical waveguide, wherein atleast one of the first, second and third suspended optical waveguideshas two fixed portions connected to the substrate and is suspendedbetween the two fixed portions; exciting a multi-slot optical modedefined in the multi-slot optical structure; and varying a width of thefirst slot and/or a width of the second slot over time.
 10. The methodof claim 9, wherein varying a width of the first slot and/or a width ofthe second slot over time comprises: moving the first optical waveguiderelative to the second optical waveguide and/or moving the third opticalwaveguide relative to the second optical waveguide.
 11. The method ofclaim 9, wherein varying a width of the first slot and/or a width of thesecond slot over time comprises: moving the first optical waveguidetowards the second optical waveguide and, simultaneously, moving thethird optical waveguide towards the second optical waveguide.
 12. Themethod of claim 11, wherein varying a width of the first slot and/or awidth of the second slot over time further comprises: moving the firstoptical waveguide away from the second optical waveguide and,simultaneously, moving the third optical waveguide away from the secondoptical waveguide.
 13. The method of claim 11, wherein moving the firstand third optical waveguides comprises moving the first and thirdoptical waveguides inside a trench in which the first, second and thirdoptical waveguides are disposed, the trench being formed in thesubstrate.
 14. The method of claim 9, wherein providing the opticalsignal to a multi-slot optical structure comprises adiabaticallycoupling the optical signal to the multi-slot optical structure using atapered optical waveguide.
 15. The method of claim 9, wherein varying awidth of the first slot and/or a width of the second slot over timecomprises applying an electrical modulating signal to a mechanicalactuator connected to the multi-slot optical structure.
 16. A method formodulating a phase of an optical signal, the method comprising:adiabatically coupling the optical signal to a multi-slot opticalstructure formed on a substrate and having first, second and thirdco-planar suspended optical waveguides arranged so that the secondoptical waveguide is positioned between the first optical waveguide andthe third optical waveguide; exciting a multi-slot optical mode definedin the multi-slot optical structure; and varying a separation betweenthe first and second optical waveguides and/or varying a separationbetween the third and second optical waveguides.
 17. The method of claim16, wherein adiabatically coupling the optical signal to a multi-slotoptical structure comprises transmitting the optical signal through atapered optical waveguide.
 18. The method of claim 16, whereintransmitting the optical signal through a tapered optical waveguidecomprises exciting an optical mode configured to laterally expand as theoptical signal propagates along the tapered optical waveguide.
 19. Themethod of claim 16, wherein varying a separation between the first andsecond optical waveguides and/or varying a separation between the thirdand second optical waveguides comprises: moving the first opticalwaveguide relative to the second optical waveguide and/or moving thethird optical waveguide relative to the second optical waveguide. 20.The method of claim 16, wherein varying a separation between the firstand second optical waveguides and/or varying a separation between thethird and second optical waveguides comprises: moving the first opticalwaveguide towards the second optical waveguide and, simultaneously,moving the third optical waveguide towards the second optical waveguide.